Weighted estimates for integral transforms and a variant of Schur's Lemma

References

• Edmunds DE, Kokilashvili V, Meskhi A. Bounded and compact integral operators. Dordrecht/Boston/London: Kluwer Academic Publishers; 2002.
   Google Scholar
• Andersen KF. Weighted inequalities for the Stieltjes transformation and Hilbert's double series. Proc Roy Soc Edinburgh Sect A. 1980;86:75–84. doi: 10.1017/S0308210500012014
   Google Scholar
• Sinnamon G. A note on the Stieltjes transformation. Proc Roy Soc Edinburgh Sect A. 1988;110:73–78. doi: 10.1017/S0308210500024860
   Google Scholar
• Bloom S. Hardy integral estimates for the Laplace transform. Proc Amer Math Soc. 1992;116:417–426. doi: 10.1090/S0002-9939-1992-1094497-X
   Web of Science ®Google Scholar
• Andersen KF. Weighted inequalities for convolutions. Proc Amer Math Soc. 1995;123:1129–1136. doi: 10.1090/S0002-9939-1995-1277088-X
   Web of Science ®Google Scholar
• Luor D-H. Hardy integral estimates for a class of integral transforms. Integral Transforms Spec Funct. 2012;23:115–127. doi: 10.1080/10652469.2011.564577
   Web of Science ®Google Scholar
• Oguntuase JA, Persson L-E, Čižmešija A. Multidimensional Hardy-type inequalities via convexity. Bull Austral Math Soc. 2008;77:245–260. doi: 10.1017/S0004972708000245
   Web of Science ®Google Scholar
• Oguntuase JA, Persson L-E, Essel EK. Multidimensional Hardy-type inequalities with general kernels. J Math Anal Appl. 2008;348:411–418. doi: 10.1016/j.jmaa.2008.07.053
   Web of Science ®Google Scholar
• Okpoti CA, Persson L-E, Sinnamon G. An equivalence theorem for some integral conditions with general measures related to Hardy's inequality. J Math Anal Appl. 2007;326:398–413. doi: 10.1016/j.jmaa.2006.03.015
   Web of Science ®Google Scholar
• Okpoti CA, Persson L-E, Sinnamon G. An equivalence theorem for some integral conditions with general measures related to Hardy's inequality II. J Math Anal Appl. 2008;337:219–230. doi: 10.1016/j.jmaa.2007.03.074
   Web of Science ®Google Scholar
• Persson L-E, Stepanov VD, Wall P. Some scales of equivalent weight characterizations of Hardy's inequality: the case. Math Inequal Appl. 2007;10:267–279.
   Web of Science ®Google Scholar
• Sinnamon G. One-dimensional Hardy-type inequalities in many dimensions. Proc Roy Soc Edinburgh Sect A. 1998;128:833–848. doi: 10.1017/S0308210500021818
   Google Scholar
• Wedestig A. Some new Hardy type inequalities and their limiting inequalities. J Inequal Pure Appl Math. 2003;4: Article 61.
   Google Scholar
• Luor D-H. On the equivalence of weighted inequalities for a class of operators. Proc Roy Soc Edinburgh Sect A. 2011;141:1071–1081. doi: 10.1017/S0308210510000776
   Google Scholar
• Aronszajn N, Mulla F, Szeptycki P. On spaces of potentials connected with Lp spaces. Ann Inst Fourier(Grenoble). 1963;12:211–306. doi: 10.5802/aif.147
   Google Scholar
• Boyd D. Best constants in a class of integral inequalities. Pac J Math. 1969;30:367–383. doi: 10.2140/pjm.1969.30.367
   Web of Science ®Google Scholar
• Boyd D. Inequalities for positive integral operators. Pac J Math. 1971;38:9–24. doi: 10.2140/pjm.1971.38.9
   Google Scholar
• Christ M. Weighted norm inequalities and Schur's Lemma. Studia Math. 1984;78:309–319.
   Web of Science ®Google Scholar
• Howard R, Schep AR. Norms of positive operators on Lp-spaces. Proc Amer Math Soc. 1990;109:135–146.
   Web of Science ®Google Scholar
• Sinnamon G. From Nörlund matrices to Laplace representations. Proc Amer Math Soc. 1999;128:1055–1062. doi: 10.1090/S0002-9939-99-05112-6
   Web of Science ®Google Scholar
• Sinnamon G. Schur's lemma and best constants in weighted norm inequalities. Matematiche(Catania). 2002;57:185–204.
   Google Scholar
• Bloom S, Kerman R. Weighted LΦ integral inequalities for operators of Hardy type. Studia Math. 1994;110:35–52.
   Web of Science ®Google Scholar
• Lai Q. Weighted modular inequalities for Hardy type operators. Proc London Math Soc. 1999;79:649–672. doi: 10.1112/S0024611599012010
   Web of Science ®Google Scholar
• Curbera GP, García-Cuerva J, Martell JM, Pérez C. Extrapolation with weights, rearrangement-invariant function spaces, modular inequalities and applications to singular integrals. Adv Math. 2006;203:256–318. doi: 10.1016/j.aim.2005.04.009
   Web of Science ®Google Scholar
• Kerman R, Torchinsky A. Integral inequalities with weights for the Hardy maximal functions. Studia Math. 1982;71:277–284.
   Web of Science ®Google Scholar
• Kokilashvili V, Krbec M. Weighted inequalities in Lorentz and Orlicz spaces. Singapore: World Scientific; 1991.
   Google Scholar
• Lai Q. Two weight Φ-inequalities for the Hardy operator, Hardy–Littlewood maximal operator, and fractional integrals. Proc Amer Math Soc. 1993;118:129–142. doi: 10.1090/S0002-9939-1993-1123665-4
   Google Scholar
• Salvador PO, Torreblanca CR. Weighted inequalities for Cesàro maximal operators in Orlicz spaces. Proc Roy Soc Edinburgh Sect A. 2005;135:1287–1308. doi: 10.1017/S0308210500004388
   Google Scholar
• Adeleke EO, Čižmešija A, Oguntuase JA, Persson L-E, Pokaz D. On a new class of Hardy-type inequalities. J Inequal Appl. 2012;2012:259. doi: 10.1186/1029-242X-2012-259
   Web of Science ®Google Scholar
• Čižmešija A, Pečarić J, Persson L-E. On strengthened Hardy and Pólya–Knopp's inequalities. J Approx Theory. 2003;125:74–84. doi: 10.1016/j.jat.2003.09.007
   Web of Science ®Google Scholar
• Heinig HP. Modular inequalities for the Hardy averaging operator. Math Bohem. 1999;124:231–244.
   Google Scholar
• Krulić K, Pečarić J, Persson L-E. Some new Hardy type inequalities with general kernels. Math Inequal Appl. 2009;12:473–485
   Web of Science ®Google Scholar
• Levinson N. Generalizations of an inequality of Hardy. Duke Math J. 1964;31:389–394. doi: 10.1215/S0012-7094-64-03137-0
   Web of Science ®Google Scholar
• Opic B, Gurka P. Weighted inequalities for geometric means. Proc Amer Math Soc. 1994;120:771–779. doi: 10.1090/S0002-9939-1994-1169043-4
   Google Scholar
• Pick L, Opic B. On the geometric mean operator. J Math Anal Appl. 1994;183:652–662. doi: 10.1006/jmaa.1994.1172
   Web of Science ®Google Scholar
• Wedestig A. Weighted inequalities for the Sawyer two-dimensional Hardy operator and its limiting geometric mean operator. J Inequal Appl. 2005;4:387–394.
   Google Scholar
• Luor D-H. A variant of a general inequality of the Hardy–Knopp type. J Inequal Pure Appl Math. 2009;10(3): Article 73, 9 pp.
   Google Scholar
• Grobler JJ, de Pagter B. Operators representable as multiplication-conditional expectation operators. J Operator Theory. 2002;48:15–40.
   Web of Science ®Google Scholar
• Lambert A. Lp multipliers and nested sigma-algebras. Oper Theory Adv Appl. 1998;104:147–153.
   Google Scholar
• Dodds PG, Huijsmans CB, de Pagter B. Characterizations of conditional expectation-type operators. Pacific J Math. 1990;141:55–77. doi: 10.2140/pjm.1990.141.55
   Web of Science ®Google Scholar
• Estaremi Y, Jabbarzadeh MR. Weighted lambert type operators on Lp spaces. Oper Matrices. 2013;7:101–116. doi: 10.7153/oam-07-05
   Google Scholar